9780131424623

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Summary

This text presents the basic theory and practice of system dynamics. It introduces the modeling of dynamic systems and response analysis of these systems, with an introduction to the analysis and design of control systems.KEY TOPICSSpecific chapter topics include The Laplace Transform, mechanical systems, transfer-function approach to modeling dynamic systems, state-space approach to modeling dynamic systems, electrical systems and electro-mechanical systems, fluid systems and thermal systems, time domain analyses of dynamic systems, frequency domain analyses of dynamic systems, time domain analyses of control systems, and frequency domain analyses and design of control systems.For mechanical and aerospace engineers.

Table of Contents

PREFACE

vii

1 INTRODUCTION TO SYSTEM DYNAMICS 1

1-1 Introduction

1

(2)

1-2 Mathematical Modeling of Dynamic Systems

3

(2)

1-3 Analysis and Design of Dynamic Systems

5

(1)

1-4 Summary

6

(2)

2 THE LAPLAGE TRANSFORM

8

(45)

2-1 Introduction

8

(1)

2-2 Complex Numbers, Complex Variables, and Complex Functions

8

(6)

2-3 Laplace Transformation

14

(15)

2-4 Inverse Laplace Transformation

29

(5)

2-5 Solving Linear, Time-Invariant Differential Equations

34

(2)

Example Problems and Solutions

36

(13)

Problems

49

(4)

3 MECHANICAL SYSTEMS

53

(53)

3-1 Introduction

53

(4)

3-2 Mechanical Elements

57

(4)

3-3 Mathematical Modeling of Simple Mechanical Systems

61

(12)

3-4 Work, Energy, and Power

73

(8)

Example Problems and Solutions

81

(19)

Problems

100

(6)

4 TRANSFER-FUNCTION APPROACH TO MODELING DYNAMIC SYSTEMS

106

(63)

4-1 Introduction

106

(3)

4-2 Block Diagrams

109

(3)

4-3 Partial-Fraction Expansion with MATLAB

112

(7)

4-4 Transient-Response Analysis with MATLAB

119

(16)

Example Problems and Solutions

135

(27)

Problems

162

(7)

5 STATE SPACE APPROACH TO MODELING DYNAMIC SYSTEMS

169

(82)

5-1 Introduction

169

(5)

5-2 Transient-Response Analysis of Systems in State-Space Form with MATLAB

174

(7)

5-3 State-Space Modeling of Systems with No Input Derivatives

181

(6)

5-4 State-Space Modeling of Systems with Input Derivatives

187

(15)

5-5 Transformation of Mathematical Models with MATLAB

202

(7)

Example Problems and Solutions

209

(30)

Problems

239

(12)

6 ELECTRICAL SYSTEMS AND ELECTROMECHANICAL SYSTEMS

251

(72)

6-1 Introduction

251

(3)

6-2 Fundamentals of Electrical Circuits

254

(7)

6-3 Mathematical Modeling of Electrical Systems

261

(9)

6-4 Analogous Systems

270

(4)

6-5 Mathematical Modeling of Electromechanical Systems

274

(7)

6-6 Mathematical Modeling of Operational-Amplifier Systems

281

(7)

Example Problems and Solutions

288

(24)

Problems

312

(11)

7 FLUID SYSTEMS AND THERMAL SYSTEMS

323

(60)

7-1 Introduction

323

(1)

7-2 Mathematical Modeling of Liquid-Level Systems

324

(8)

7-3 Mathematical Modeling of Pneumatic Systems

332

(5)

7-4 Linearization of Nonlinear Systems

337

(3)

7-5 Mathematical Modeling of Hydraulic Systems

340

(8)

7-6 Mathematical Modeling of Thermal Systems

348

(4)

Example Problems and Solutions

352

(23)

Problems

375

(8)

8 TIME-DOMAIN ANALYSIS OF DYNAMIC SYSTEMS

383

(48)

8-1 Introduction

383

(1)

8-2 Transient-Response Analysis of First-Order Systems

384

(4)

8-3 Transient-Response Analysis of Second-Order Systems

388

(11)

8-4 Transient-Response Analysis of Higher Order Systems

399

(1)

8-5 Solution of the State Equation

400

(9)

Example Problems and Solutions

409

(15)

Problems

424

(7)

9 FREQUENCY-DOMAIN ANALYSIS OF DYNAMIC SYSTEMS

431

(60)

9-1 Introduction

431

(1)

9-2 Sinusoidal Transfer Function

432

(6)

9-3 Vibrations in Rotating Mechanical Systems

438

(3)

9-4 Vibration Isolation

441

(6)

9-5 Dynamic Vibration Absorbers

447

(6)

9-6 Free Vibrations in Multi-Degrees-of-Freedom Systems

453

(5)

Example Problems and Solutions

458

(26)

Problems

484

(7)

10 TIME-DOMAIN ANALYSIS AND DESIGN OF CONTROL SYSTEMS

491

(117)

10-1 Introduction

491

(3)

10-2 Block Diagrams and Their Simplification

494

(7)

10-3 Automatic Controllers

501

(5)

10-4 Transient-Response Analysis

506

(7)

10-5 Transient-Response Specifications

513

(9)

10-6 Improving Transient-Response and Steady-State Characteristics

522

(16)

10-7 Stability Analysis

538

(7)

10-8 Root-Locus Analysis

545

(17)

10-9 Root-Locus Plots with MATLAB

562

(4)

10-10 Tuning Rules for PID Controllers

566

(10)

Example Problems and Solutions

576

(24)

Problems

600

(8)

11 FREQUENCY-DOMAIN ANALYSIS AND DESIGN OF CONTROL SYSTEMS

608

(87)

11-1 Introduction

608

(1)

11-2 Bode Diagram Representation of the Frequency Response

609

(20)

11-3 Plotting Bode Diagrams with MATLAB

629

(1)

11-4 Nyquist Plots and the Nyquist Stability Criterion

630

(10)

11-5 Drawing Nyquist Plots with MATLAB

640

(3)

11-6 Design of Control Systems in the Frequency Domain

643

(25)

Example Problems and Solutions

668

(22)

Problems

690

(5)

APPENDIX A SYSTEMS OF UNITS

695

(5)

APPENDIX B CONVERSION TABLES

700

(5)

APPENDIX C VECTOR-MATRIX ALGEBRA

705

(15)

APPENDIX D INTRODUCTION TO MATLAB

720

(37)

REFERENCES

757

(2)

INDEX

759

Excerpts

A course in system dynamics that deals with mathematical modeling and response analyses of dynamic systems is required in most mechanical and other engineering curricula. This book is written as a textbook for such a course. It is written at the junior level and presents a comprehensive treatment of modeling and analyses of dynamic systems and an introduction to control systems.Prerequisites for studying this book are first courses in linear algebra, introductory differential equations, introductory vector-matrix analysis, mechanics, circuit analysis, and thermodynamics. Thermodynamics may be studied simultaneously.Main revisions made in this edition are to shift the state space approach to modeling dynamic systems to Chapter 5, right next to the transfer function approach to modeling dynamic systems, and to add numerous examples for modeling and response analyses of dynamic systems. All plottings of response curves are done with MATLAB. Detailed MATLAB programs are provided for MATLAB works presented in this book.This text is organized into 11 chapters and four appendixes. Chapter 1 presents an introduction to system dynamics. Chapter 2 deals with Laplace transforms of commonly encountered time functions and some theorems on Laplace transform that are useful in analyzing dynamic systems. Chapter 3 discusses details of mechanical elements and simple mechanical systems. This chapter includes introductory discussions of work, energy, and power.Chapter 4 discusses the transfer function approach to modeling dynamic systems. Transient responses of various mechanical systems are studied and MATLAB is used to obtain response curves. Chapter 5 presents state space modeling of dynamic systems. Numerous examples are considered. Responses of systems in the state space form are discussed in detail and response curves are obtained with MATLAB.Chapter 6 treats electrical systems and electromechanical systems. Here we included mechanical-electrical analogies and operational amplifier systems. Chapter 7 deals with mathematical modeling of fluid systems (such as liquid-level systems, pneumatic systems, and hydraulic systems) and thermal systems. A linearization technique for nonlinear systems is presented in this chapter.Chapter 8 deals with the time-domain analysis of dynamic systems. Transient-response analysis of first-order systems, second-order systems, and higher order systems is discussed in detail. This chapter includes analytical solutions of state-space equations. Chapter 9 treats the frequency-domain analysis of dynamic systems. We first present the sinusoidal transfer function, followed by vibration analysis of mechanical systems and discussions on dynamic vibration absorbers. Then we discuss modes of vibration in two or more degrees-of-freedom systems.Chapter 10 presents the analysis and design of control systems in the time domain. After giving introductory materials on control systems, this chapter discusses transient-response analysis of control systems, followed by stability analysis, rootlocus analysis, and design of control systems. Finally, we conclude this chapter by giving tuning rules for PID controllers. Chapter 11 treats the analysis and design of control systems in the frequency domain. Bode diagrams, Nyquist plots, and the Nyquist stability criterion are discussed in detail. Several design problems using Bode diagrams are treated in detail. MATLAB is used to obtain Bode diagrams and Nyquist plots.Appendix A summarizes systems of units used in engineering analyses. Appendix B provides useful conversion tables. Appendix C reviews briefly a basic vector-matrix algebra. Appendix D gives introductory materials on MATLAB. If the reader has no prior experience with MATLAB, it is recommended that he/she study Appendix D before attempting to write MATLAB programs.Throughout the book, examples are presented at strategic points so that the reader will have a bett